using @Hazza's idea, you could make a couple of minor changes to the contrib module to allow a user to edit their own profile..
For example:-
In the Contrib module, inside the Views Folder create EditorTemplates folder, then create a Parts folder inside that. Add a User.Edit.cshtml to the parts folder with the following markup.

You will need to add a reference to the Orchard.Users module, and inject a couple of extra services to make this work.. But a variation of this was used by our company to get users edit access to their profiles..
Disclaimer:- The User.Edit.cshtml and the code for the Edit and EditPost are just copied from the Orchard.User module from it's Admin controller..